Gambling tests for pseudorandom number generators

This paper extends the idea of serial tests by employing a carefully selected dimension reduction which is equivalent to playing a gambling strategy in a fair coin flipping game. We apply the generalized φ-divergence for testing the hypothesis that the simulated coin is fair and memoryless. An application to twisted GFSR generators shows the ability of our test to detect deviations from equidistribution in high dimensions.

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